# If a bowl contains ten hazelnuts and eight almonds, what is the probability that four nut randomly selected from the bowl will all be hazelnuts?

We can model the bowl of nuts with a hypergeometric distribution containing 10 "successes" (hazelnuts) and 8 "failures" (almonds).

The formula we want to use is

Where:

Then the probability of getting 4 hazelnuts in a random sample of 4 nuts is:

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The probability of selecting four hazelnuts from the bowl is ( \frac{{\binom{10}{4}}}{{\binom{18}{4}}} ), which simplifies to ( \frac{{210}}{{3060}} ), or approximately 0.0686, or 6.86%.

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